This paper considers volume-conserving shape changes of small faceted particles or cavities; these changes are driven by surface-energy reduction. If these changes require normal motion of the facets (singular surfaces), and if the perimeter free energy sigma(p) (per unit area) of a nucleus of a new beet layer is comparable to a typical surface free energy (sigma approximate to 1 J/m(2)), the energy barrier is prohibitively large for facets larger than a limiting size of approximately a nanometer unless they are intersected by dislocations that provide a source of steps. In the absence of such dislocations, particles that contain these facets are immobilized in their initial shapes. If sigma(p) < sigma, the limiting facet size is increased by a factor of approximately sigma/sigma(p).